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Posted by **Miley** on Thursday, May 8, 2008 at 8:32pm.

1/2log base 4 25-2(3logbase4 5-log base 4 25)

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**Damon**, Thursday, May 8, 2008 at 8:48pm.5 log4 5^2 = log4(5)

2(3 log4 5 - 2 log4 5 ) = 2 log4 5

so we have

-1 log4(5)

= log4(.2)

that might be the answer you are looking for but if you need a number

4^x = .2 ?

x ln 4 = ln .2

x = 1.39/-1.61

= - .863

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**Miley**, Thursday, May 8, 2008 at 8:53pmI have to condense it... thanks for your help

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**Reiny**, Thursday, May 8, 2008 at 8:50pm1/2log base 4 25-2(3logbase4 5-log base 4 25)

= 1/2 log_{4}25 - 2(3log_{4}5 - log_{4}25)

= log_{4}5 - 2(log_{4}125 - log_{4}25)

= log_{4}5 - 2(log_{4}(125/25)

= log_{4}5 - 2log_{4}5

= -log_{4}5

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**Miley**, Thursday, May 8, 2008 at 8:55pmmy teacher has a different answer... she has log base 4(1/25).

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**Damon**, Thursday, May 8, 2008 at 9:07pmWell, I think log4 (1/5)

I got -1 log4 5

she got -2 log4 5

one of us subtracted wrong or something

However Reiny and I agree exactly, so the odds are in our favor :

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**Miley**, Thursday, May 8, 2008 at 9:10pmmy teacher got log base 4 (1/125) and it's a quiz review sheet, and all the math teachers look over it... sooo... I get how to simplify the 1/2 part but how do i condense the parenthesies

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**Reiny**, Thursday, May 8, 2008 at 9:15pmWell, Miley, if you typed your question correctly, then your teacher is wrong.

Even though both Damon and I did it slightly differently, we came up with the same answer.

I evaluated your original expression the way it stands on my calculator, and got the same result as our answer at the end.

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**Damon**, Thursday, May 8, 2008 at 9:12pmBy the way, your teacher and I both said

-n log4 x = log4 x^-n = log4 (1/x^n)

which is how we converted the negative log to positive

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**Miley**, Thursday, May 8, 2008 at 9:14pmcan you please show me how to condense -2(3logbase 4 5-log base 4 5), thanks:)

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**Damon**, Thursday, May 8, 2008 at 9:17pmI do not know what to say. Reiny and I did the parentheses quite different ways and both got the same answer.

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**Miley**, Thursday, May 8, 2008 at 9:18pmCan you please break it down step by step and show me how you did it! thanks:)

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**Damon**, Thursday, May 8, 2008 at 9:21pmYou have two ways to condense the inside the parentheses up there

I did it by saying log 25 = 2 log 5

Reiny did it by saying

log 125 - log 25 = log (125/25) = log 5

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**Damon**, Thursday, May 8, 2008 at 9:31pm-2(3logbase 4 5-log base 4 5)

Hey, that is not what you wrote in the original question

that is just -2 (2 log4 5)

which is

-4 log4 of 5

NOW

log4 5 - 4 log4 5

= -3 log4 5

= log4 (1/5^3)

= log4 (1/125)

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**aleah**, Friday, May 9, 2008 at 12:12amUh...I'm posting this one on gothomework.tk